Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2005-08-15
Nonlinear Sciences
Exactly Solvable and Integrable Systems
16 pages
Scientific paper
Scaling symmetry of gl_n-type Drinfel'd-Sokolov hierarchy is investigated. Applying similarity reduction to the hierarchy, one can obtain the Schlesinger equation with (n+1) regular singularities. Especially in the case of n=3, the hierarchy contains the three-wave resonant system and the similarity reduction gives the generic case of the Painleve VI equation. We also discuss Weyl group symmetry of the hierarchy.
Kakei Saburo
Kikuchi Tetsuya
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